Constant output characteristics and design methodology of double side LC compensated capacitive power transfer

Capacitive power transfer (CPT) has been verified to be capable of transferring a power level as high as inductive power transfer (IPT) recently, and has its own merits. It is a well complement of IPT in near-field wireless power transfer (WPT). This paper gives a newly designed method of realizing both constant output voltage (COV) and constant output current (COC) modes of double side LC compensated CPT. Firstly, through analysis of basic circuit characteristics, the conditions for both of the two modes are deduced theoretically. Especially, one merit of the method is that the conditions indicate a very clear relationship between the compensation components forming resonant tanks. Another merit is that the couple capacitors also participate in resonant tanks. Different from the COV mode, the COC mode can theoretically reach zero phase angle condition simultaneously. Based on these conditions, the parameter design methodology is proposed. Besides, an efficient model of double side LC compensated CPT is built, and the optimum load is calculated theoretically to guide the design course. Finally, the results of both simulations and experiments demonstrate high consistency with the theoretical analysis.


Results
Theoretical model and analysis. A double side LC compensated CPT mainly falls into seven parts, as shown in Fig. 1. Supposing that the input power is a DC source, it should be changed into a high frequency AC that can resonant in the tank of the primary LC compensation net, triggering a high flux electric field between the couple plates, and causing a displacement current from the emission plates of the coupler to the receiving plates. Then, the electricity power going through the coupler will be stored temporarily in the resonant tank of the secondary LC compensation net, providing a source to feed the rectifier and drive the load.
The proposed CPT can be simplified as Fig. 2a. The output of the inverter is treated as a high frequency input voltage in Fig. 2a. When the horizontal distance between plates is significant enough, the cross-couple capacitance can almost be negligible and the couple capacitance is just the capacitance formed by each pair of plates. C o is defined as the capacitance formed by odd plates P1 and P3, and C e is the capacitance formed by plates P2 and P4. When taking consideration of the cross-couple capacitance between each two plates, the equivalent model www.nature.com/scientificreports/ of the coupler is proposed in reference 14 , shown in the blue pane in Fig. 2b. The load resistance sourced by the rectifier with a parallel capacitor filter can be equivalent to R eq by 8R L /π 2 19 . In Fig. 2b, suppose C 1 = C 1_ext + C 1_in and C 2 = C 2_ext + C 2_in . Thus, a further simplified equivalent circuit in Fig. 2c is derived.

Analysis of constant output characteristics.
Almost all appliances use electricity as power supply expect a constant input to gain a normal rated power. In this part, the constant output characteristics, including COC and COV, will be exploited based on the equivalent models given in the former part.
A. COV mode The schematic in Fig. 2a can be divided in two symmetrical parts by the dashed blue line shown in Fig. 3a,b. Figure 3c is a change form of Fig. 3b, with only a position change in L 2 . Supposing that the operation frequency of the system is ω, the voltage U 1_out in Fig. 3a can be defined by (1), and the voltage U out in Fig. 3b can be defined by (2).
In (1) and (2), Combine (1) and (2), a special voltage gain can be derived by (4) when (3) is met. It is clear that the voltage gain G V of the CPT has no relationship with R eq in (4), indicating a constant voltage output of CPT. Thus, Eq. (3) is the condition for COV mode, and it indicates that L 1 is in resonance with the parallel capacitance of C 1 and C o , and L 2 is in resonance with the parallel capacitance of C 2 and C e . The resonant tanks are marked in blue panes in Fig. 3. According to (4), the output power is defined by (5).
In (4), C 1 = λ 1 C o and C 2 = λ 2 C e . B. In Fig. 2c, resistance Z 1 , Z 2 , Z 3 can be expressed by (6), (7) and (8). Combining (6), (7) and (8), Z 2 and Z in can be derived by (9) and (10). To achieve zero phase angle, the input impedance should be purely resistant. In this case, the vector of numerator and denominator in Eq. (10) should have the same angle, a special situation is that the condition in (11) is met. Equation (11) can be changed into (12). From (12), it is easy to find that the inductance L 1 and a combination of capacitance that C 2 in serial with C M , then in parallel with C 1 , form a resonant tank in the primary part. Similarly, L 2 and C 1 , C 2 , C M form another resonant tank in the secondary part. The resonant tanks are exhibited in Fig. 4. The equivalent capacitance of the coupler takes part in both primary and secondary resonant tanks. Substituting (11) into (10), we can get (13).

(a)
Then, voltage of C 1 , C 2 , and U out can be expressed by (14), (15) and (16), respectively. Combining (6), (13), (14), (15) and (16), the output voltage can be derived from (17). Current of load resistance R L can be expressed by (18) when C 1 = k 1 C M and C 2 = k 2 C M . It can be intuitively seen that the output current of the proposed CPT has no relationship with the load resistance. The power on the load resistance can be defined by (19), which demonstrates that the output power is defined positively by the square of the angular frequency ω and the load resistance. www.nature.com/scientificreports/ C. Analysis of DC-DC efficiency From the conclusion above, it is known that the zero phase angle can be achieved in COC mode, making zero voltage switching (ZVS) possible to realize. However, ZVS cannot be achieved in COV mode. Therefore, the COC mode is chosen to analyze the system efficiency. The method for COV mode is similar.
The parasitic resistance of each component in the system is needed to be analyzed when establishing the efficiency model. However, the impact of parasitic resistance from couple capacitors can be limited by choosing high quality factor capacitors C 1 , C 2 . The non-core inductance winded by litz wire should be adopted to reduce iron-core loss and serial parasitic resistance caused by skin effect when the system works at a high frequency. But a long litz wire will bring non-negligible parasitic resistance. Parasitic resistance also exists in the inverter and rectifier, known as turn-on resistance. In addition, energy loss in the inverter and rectifier also includes switching loss that is much more complex than the turn-on loss, and it has already been well studied 34 . Here, ZVS is supposed to be realized and the switching loss is negligible. Supposing that the parasitic resistance of inverter and L 1 contributes to R L1, rectifier and L 2 contributes to R L2 , shown in Fig. 5a. To simplify the analysis, R L2 and R eq can be considered as a whole, R′ eq . In Fig. 5b, circuit in the red dash line frame can be treated as an impedance Z′ in in Fig. 5c. Based on the assumption above, the system power loss can be calculated by (20). Therefore, the system efficiency can be calculated by (21). The derivation of η can be expressed in (22). It can be easily defined that the system efficiency has a maximum optimum value η max when R′ eq has the value R′ eq_opt , calculated by (23).
In (20), In (21), www.nature.com/scientificreports/ Design methodology. According to the analysis above, the general design methodology is discussed in this part. Before designing a CPT, the basic demands like nominal input, rated output and physical dimensions allowed for the coupler should be acquired.
A. Parameter design for COV mode If the rated voltage demand U in , U out is given, the voltage gain is clear. Then, suitable compensation capacitors C 1 and C 2 can be chosen. So the coupler capacitance C o , C e can be defined by (4). Then, the coupler size can be calculated by ε*S/d. The sizes of the couple plates are often restricted by the available volume of a certain appliance. Thus, to gain a considerable capacitance, a trade-off between the transfer distance and the size of the coupler should be made. If the calculated coupler size is bigger than the allowed range, we should return to choose C 1 and C 2 . Otherwise, the procedure will continue to choose a suitable operation frequency f. Then the value of inductors L 1 and L 2 can be calculated. Volume and parasitic resistance of L 1 , L 2 is another constraint. Because the parasitic equivalent serial resistance R L1 and R L2 is positively related to the value of L 1 , L 2 . If the efficiency η is not higher than the expected or designed value η exp , the procedure will go back to choose C 1 and C 2 , or f. After defining L 1 , L 2 , MOSFETs for the inverter and diodes for the rectifier should be chosen according to the frequency, voltage, and current. The procedure of parameter design for a COV CPT system is concluded in Fig. 6. B. Parameter design for COC mode The procedure of parameter design for COC CPT system is similar to that of a COV system. However, the difference is that the output current is directly proportional to the angular frequency ω, so when choosing C 1 , C 2 and f, a trade-off should be made between them. Another trade-off is between the coupler size or transfer distance and the couple capacitance. Especially the output current and power is negatively related to the mutual couple capacitance C M . However, according to the (21), the system efficiency is in positive relationship with C M . A smaller couple capacitance will also require a higher operation frequency or larger resonant inductor, which will trigger a high voltage stress between plates.
These design methodology will be verified in the next section by simulation and experiments. The DC-to-DC efficiency of the system will also be verified.
Simulations and experiments. The constant output characteristics and design methodology are verified through MATLAB simulations and experiment tests. Table 1 gives the parameters designed by the proposed methodology.
Firstly, The system parameters in Table 1 are used to calculate the output characteristics of the system directly in MATLAB. Then, an experiment prototype in Fig. 7 is built for further verification. In this prototype, a DSP board serves as PWM generator, N-Channel SiC MOSFET LSIC1MO120E0080 is adopted to form the full-bridge www.nature.com/scientificreports/ inverter, litz wire is used for all connections in the high frequency part to minimize the loss caused by skin effect. The coupler is made by four aluminum plates with the size shown in the Table 1. Gap distance between each pair of plates is filled with a plastic paper (0.05 mm in thickness) to enhance the capacitance of the coupler. In fact, this experiment prototype aims at verifying the constant output characteristics of the suggested system, so the affection from transfer distance is not studied. Numerical quantity of each component in the experiment platform is measured by high-precision LCR Meter, shown in Table 2.
A. COV mode MATLAB simulation results are presented in Fig. 8. It is demonstrated that the system efficiency increases firstly and then decreases with the increase of R L in Fig. 8a, and the optimum load resistance is about 5Ω. The maximum efficiency is 90.4%, which is in good accordance with the theoretical analysis. Both the amplitude and absolute value of angle of the total input impedance Z in increase with R L , but the trends become slow. Especially, the angle of Z in is negative, which indicates Z in is capacitive, and zero phase angle cannot be achieved. However, the output voltage shows a constant value of about 60 V when R L is above 5Ω. Figure 8b is the response of the system against the system frequency when R L is 20Ω. Curves in Fig. 8b indicate that the compensation net is intrinsically a band-pass filter.  Figure 7. Experiment platform. Taken by the first author Qiao Xiong,through the digital camera of mobilephone, and the descriptive text is added by the software "Microsoft Office Visio 2013" url: https:// www. micro soft. com/ zh-cn/ micro soft-365/ previ ous-versi ons/ micro soft-visio-2013.  Fig. 9a is taken by ZLG Power Analyzer. Due to the voltage drop caused by the parasitic resistance of switch devices, the tested output voltage is slightly lower than simulation. It also shows an DC to DC efficiency of 81.23% when R L is 15Ω, close to Fig. 8a. The system efficiency is not so high, due to the significant angle of the total input impedance, and ZVS condition can't be achieved, either. The black curve in Fig. 9b shows the output voltage changes with R L , which indicates a tiny increase when the load resistance increasing, due to the decrease of current level in the whole system. The red curve in Fig. 9b exhibits that the DC-to-DC efficiency of the COV system decreases with the increase of R L . This phenomenon is in good accordance with the trend of the total input impedance angle shown in Fig. 8a. B. COC mode Curves drawn by MATLAB in Fig. 10 demonstrate that the total input impedance angle is very close to zero when R L is more than 5Ω. This means that the zero phase angle and ZVS condition are possible to achieve. The last curve in Fig. 10 shows that the output voltage increase linearly with R L . This means a fine constant output current is achieved. Response of the system when frequency changes in COC mode is similar to the COV mode.
The output waveform of the inverter taken by the oscilloscope is exhibited in Fig. 11. The current waveform slightly lags behind the voltage, indicating ZVS condition is achieved. The DC-to-DC efficiency of the COC system can always reach above 87%. Figure 12a shows an efficiency of 88.46% when R L is 25Ω and U in is 58.828 V. The black curve in Fig. 12b indicates the output current is relatively constant when R L varies and U in is set to about 58.828 V, and the red curve shows almost the same trend with the simulation results in the first diagram in Fig. 10. The difference between Figs. 10 and 12b is mainly because the energy loss of the inverter and the rectifier in Fig. 10 has not been taken into consideration. Experiments have also verified that the system efficiency can easily reach above 90% when the DC source provides a voltage more than 100 V.

Discussion
A. Safety issues The electromagnetic safety property of CPT system is often doubted. Some researches 9,29 have been carried out to investigate it. Nevertheless, safety is a relevant definition. It is undeniable that the electric field in the area between couple plates and in the very nearby area is so high that it may exceed the criterion of the IEEE C95.1 standard 35 . However, the electric field decreases very rapidly with distance 19 . Safety can be ensured except for the dangerous areas. It is pointed out that the dangerous area is within 350 mm while the couple capacitance is only 2.8 pF and the voltage between plates reaches as high as 1.73 kV 19 . The couple capacitance can be enhanced through many approaches, like coating metallic plates with a very thin high permittivity material, and letting them rely on each other to shorten the distance between plates. Bigger couple capacitance will ensure a lower voltage stress on the plates, thus the dangerous area will be further restricted. Many other approaches can also be applied to ensure safety, like physical isolation to keep the organisms out of dangerous areas, newly designed configuration of the coupler to restrict the power emitted by couple plates. B. Switch between COV and COC mode In some cases, switching between COV and COC is required. For example, the course of charging a battery is usually COC first, and COV at the end. According to the proposed decoupling method, the COV and COC system can be designed with a little difference in L 1 , L 2 only. Thus, to switch between COV and COC modes, a control loop like Fig. 13 shows can be built. The inductor L 1 and L 2 can be divided into two parts in Fig. 13, L′ 1 and L′ 2 represent the inductance difference between COV and COC modes. The control loop contains a sampler, a tester, a comparator, a driver and two switches S 1 , S 2 .
Suppose CPT system works in COC mode at first, and S 1 , S 2 is open. When the voltage reaches a value near the full voltage of the battery, this signal will be sampled and then tested. This tested value will be compared with the predefined voltage point for switching charge mode and then a decision will be made to close S 1 , S 2 . It should be noted that a communication path needs to be established between the primary and secondary parts to transfer the control signal. Another way to switch between COV and COC mode is to change the operation frequency. Supposing that all compensation components are designed, so the frequency of COV and COC modes can be expressed as (24). When switching between COV and COC mode is required, it is just needed to switch the PWM signal between the frequency f COV and f COC .
C. Output stability in response to different compensation parameters and current gain G i It is a common sense that parasitic resistance exists in each component in spite of sparing no effort to reduce it. The parasitic resistance would affect the input or output characteristics of the circuit more or less. The affection by different groups of system parameters and current gain G i is evaluated through MATLAB simulation using the parameters listed in Table 3. The results are shown in Fig. 14. By comparing the curves in Fig. 14, it can be concluded that a smaller G i will induce a more stable output current and efficiency.

Conclusion
This paper introduces a newly designed load decoupling method that can achieve both COV and COC mode in double side LC compensated CPT. Through the analysis of basic circuit characteristics, the conditions for both two modes are determined. The proposed method has following three advantages: Besides, an efficient model of double side LC compensated CPT is built, and the optimum load is calculated theoretically based on the model. Based on the constant output conditions and efficient model, the parameter design methodology is proposed. Results of both simulations and experiments demonstrate high agreement with the theoretical analysis. Finally, three practical issues are discussed, including electromagnetic safety, switching between the two modes, and stability of output with different groups of parameters. In future research work, we will concentrate on the reduction of parameter sensitivity and optimization of compensation net, efficiency improving scheme and stability control, and the mechanism of transferring power in seawater.

Iout[A]
Iout change with RL